Let's hope your friend really did cycle it. But to be on the safe side, test you water asap and post your ammonia, nitrites and nitrates. Ammonia and nitrites are the most toxic to your fish. If the tank was cycled, you should not have any ammonia or nitrites, but may have some nitrates. Nitrates are not toxic at low levels. If you see any ammonia or nitrite, this is a bad sign and good indicator that the tank has not finished cycling. Which means your fish may be in danger.
If you do not have a complete test kit, go to your local fish store tomorrow with a water sample. They will test your water for free and you can pick up a liquid test kit while you are there to better monitor your water conditions.
I would start by doing a 50% water change today, to be cautious. Match the temperature of the water to what is currently in the tank. Use your thermometer to do this. Be sure to use a water conditioner to dechlorinate your water as chlorine is also toxic as I am sure you may know. I am only adding some of these details in case you are new to fish keeping. If you already know, my apologies for being redundant. Just want to help
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I would continue doing 20% water changes daily for a week if your tank is cycled, meaning for sure it has no ammonia or nitrites. After which I would continue doing 20% water changes every 2-3 days until the fins look healthy and healing again.
If however your tank was not completely cycled you will need to do a bit more work by doing water changes to keep you nitrites and ammonia as low as possible for the sake of your fish. Depending on how high the levels are you may need to do more aggressive water changes.
Some other things to consider are getting some aquarium salt when you go to the fish store. You will want to add one tablespoon per 5 gallons. Predissolve the salt into water that you add for your water changes. This will promote healing as well as elevating the temperature in the tank. Tetras like temp between 75-82ish. If you have a tank heater you will want to gradually raise the temperature. If your tank is already around 80F, then just leave it there. If you do not have a heater for your size tank a heater will be fairly inexpensive for a tank of your size. Lastly, if you have a fish that looks really bad off you may wish to isolate them from the others. You can invest in a breeder box. They generally cost less than $5. Breeder boxes are small plastic floating boxes or netted cages that fit in your tanks that allow you to isolate a fish. These are merely suggestions. The best medicine is clean conditioned water.
Keep us posted. I hope your little guys heal up soon.